This invention relates to communication systems and methods and, more particularly, to communication systems and methods in which multiple versions of a signal are processed to detect the signal.
In most communication systems, it is beneficial to understand how a communication signal changes as it progresses from a transmitter to a receiver. Conceptually, the cumulative variations that a communication signal experiences is characterized in the art as a “channel.” The concept of a digital communications channel is well known. In particular, it is known that a channel can affect the amplitude and phase of a signal in the channel. As a simple example, suppose a signal cos(ω0t′) is communicated in a channel, where w0 is the angular frequency of the signal, t′ is the time associated with the transmission of the signal, and t′=0 represents the beginning of the transmission. Ideally, the signal that arrives at a receiver should have the same amplitude and phase; i.e., the received signal should be cos(ω0t), where t is the time associated with receiving the signal, and t=0 represents the beginning of the reception. The time t=0 may correspond to t′=π, for some transmission delay π. However, the received signal is seldom the same as the transmitted signal, even in a noiseless environment. Rather, (in the absence of noise) a receiver will more likely receive a signal A cos(ω0t+φ), where A is a real number that shows the channel's effect on the amplitude of the signal, and φ is a real number that shows the channel's effect on the phase of the signal. The quantity φ is commonly referred to as “initial phase.”
Although the example above shows a transmission signal that has only one frequency component ω=ω0, a signal may include more than one frequency component. Additionally, a channel may affect each frequency component differently. Accordingly, the amplitude A and the initial phase φ in the example above may only apply to frequency component ω=ω0. From this point on, when a signal includes more than one frequency component, the amplitude and initial phase for each frequency component ω=ωi will be denoted with a corresponding subscript i.
A fundamental concept of digital communications is that amplitude and initial phase can be represented by a coordinate in a Cartesian plane. For example, an amplitude A and an initial phase φ can be represented by the coordinate (x,y) where x=A cos(φ) and y=A sin(φ). Conversely, given a coordinate (x,y), an amplitude and initial phase can be computed by A=√{square root over (x2+y2)} and
  ϕ  =            arctan      ⁡              (                  y          x                )              .  Another fundamental concept is that a coordinate (x,y) can also correspond to a complex number of the form (x+jy), where j is the imaginary unit. In this case, the x-axis represents the real part of a complex number, and the y-axis represents the imaginary part of a complex number. The benefits of representing amplitude and initial phase graphically as a coordinate point and mathematically as a complex number are that these representations allow changes in amplitude and initial phase to be easily illustrated and computed. The next paragraph shows an example of computing a channel's effects on a signal's amplitude and initial phase. In particular, an important computation involves Euler's formula, which states that a complex number (x+jy) can equivalently be expressed as Aejφ, where e is the complex exponential, and, as shown above, A=√{square root over (x2+y2)} and
      ϕ    =          arctan      ⁡              (                  y          x                )              ,X=A cos(φ) and y=A sin (φ).
As an example, suppose a transmitted signal in a channel has frequency components of the form Ai cos(ωit+φi). In the absence of noise, the channel will generally alter the amplitude multiplicatively by a factor Ki, and alter the initial phase additively by a factor θi, resulting in a received frequency component of the form KiAi cos(ωit+φi+θi). Representing these amplitudes and initial phases mathematically, the amplitude and initial phase of the transmitted frequency components can be characterized by Aiejφi, and those of the received frequency component can be characterized by KiAiej(φiθi)=AiejφiKiejθi. This shows two important things. First, it can be seen that the channel's effect on the amplitude and initial phase of the transmitted frequency component is captured by the term Kiejθi. Second, if (in the absence of noise) the amplitude and initial phase of a received frequency component are Biejφi, then the channel's effect on the transmitted amplitude and initial phase can be computed by
                    K        i            ⁢              ⅇ                  jθ          i                      =                                        B            i                    ⁢                      ⅇ                          jφ              i                                                            A            i                    ⁢                      ⅇ                          jφ              i                                          =                                    B            i                                A            i                          ⁢                  ⅇ                      j            ⁡                          (                                                φ                  i                                -                                  ϕ                  i                                            )                                            ;i.e.,
      K    i    =            B      i              A      i      and θi=φi−φi. When all of the effects Kiejθi across a continuous frequency range are quantified, the result is a function showing a channel's effect on signal amplitude and initial phase based on frequency. The function is referred to in the art as a “transfer function.” A graph of a transfer function with respect to frequency is referred to as the channel's “frequency response.”
It is known that a channel's frequency response can change over time. Therefore, the channel's frequency response may need to be estimated periodically in order to maintain a reasonably accurate estimate of the frequency response. In some situations, the changes may occur randomly and channel estimates may momentarily become inaccurate. One process that can supplement channel estimation in such situations is known in the art as “diversity.” Diversity involves sending multiple versions of a communication signal to a receiver in multiple channels where, ideally, the channel estimate for at least one of the channels is reasonably accurate. To accomplish this, diversity requires the multiple channels to be substantially uncorrelated so that changing conditions in one channel do not also occur in another channel. A receiver can receive and process these different versions to detect the communication signal. In some cases, the receiver can simply select the version that has the highest signal energy to be the detected signal. In some cases, the receiver can combine the multiple versions in equal or unequal proportions to produce the detected signal.
Although diversity is beneficial, its implementation is also correspondingly more complex. In some situations, a communication system may not need the full benefit of diversity. For example, some communication systems may be able to tolerate more inaccuracy in the detected signal and may benefit more from a less complex implementation. Accordingly, there is continuing interest in further developing the technology of diversity communication and its implementation.